Multiple choice

X, Y and Z invested their capitals in the respective ratio of 4 : 8 : 5. At the end of the year, X, Y and Z received their shares of profit in the respective ratio of 2 : 3 : 4. Find the ratio of times for which they invested their money?

  1. X : Y : Z = 3 : 4 : 2

  2. X : Y : Z = 6 : 11 : 9

  3. X : Y : Z = 20 : 15 : 32

  4. X : Y : Z = 12 : 16 : 9

  5. X : Y : Z = 15 : 18 : 32
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Profit = Investment * Time. Time = Profit / Investment. X_time = 2/4 = 0.5. Y_time = 3/8 = 0.375. Z_time = 4/5 = 0.8. Ratio: 0.5 : 0.375 : 0.8. Multiply by 40: 20 : 15 : 32.

AI explanation

The profit sharing ratio is the product of the capital ratio and the time ratio. Setting up the equation (4 * Time X) : (8 * Time Y) : (5 * Time Z) equals the profit ratio 2 : 3 : 4. Solving for the individual times shows that Time X is 0.5, Time Y is 0.375, and Time Z is 0.8. Converting these values to the simplest whole number ratio gives X : Y : Z = 20 : 15 : 32.

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